Let PA(n,d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m,p^m-1k) for a given prime number p, a positive integer k<p and a positive integer m. The resulted array has (|PA(p,k)|·p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k≥2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA(p^m,p^m-1k) for a given index i very simply.